As someone who recently did a character transfer of my own, I have to admit I was nervous about the transfer considering some of the horror stories that I'd heard about long transfers, multiple charges despite cards being rejected, and more. However, it would appear that Blizzard has decided to take the entire process of Paid Character Transfers offline while they see what they can do about fixing it.

Per Pavonum on the Customer Service Forums:

As some of you have already noticed, the Paid Character Transfer service has been temporarily shut down so that further efforts may be made to ensure that its correct functionality is restored; our developers are currently working to repair the underlying coding issues that have contributed to the present complications for many players. While it is not known at this time when further updates shall become available, you may rest assured that we shall make you aware with all due haste at that time; for now, we are greatly appreciative of your continued patience. Thanks, folks. :)

Obviously this isn't going to do much for those who have already had problems of getting multiple charges or characters caught in limbo between realms. But I am very glad to see that Blizzard is taking the system offline and checking to see what they can do to fix these problems moving forward from this point. Personally, I'd be willing to wait for however long they need to make sure the overcharge bug is 100% fixed.